1. Field of Invention
The present invention is directed towards methods of creating and optimizing images in a catadioptric projector system. More specifically, the present invention presents methods of addressing defocus and distortion issues in projected images, and particularly in images projected using reflector and/or refractor materials.
2. Description of Related Art
High resolution and high contrast projectors are increasingly used in a wide array of commercial and scientific applications, ranging from shape acquisition, to virtual environments and Imax© theaters. In vision and graphics applications, cameras are often combined with projectors to form a projector-camera, or ProCam, system, for creating so-called “intelligent projection systems”. Previous work puts forth a vision of intelligent projection systems serving as novel tools for problem solving. Using pre-authored 3D models of objects, shader lamps have been used to add virtual texture and animation to real physical objects with non-trivial, complicated shapes. It is also possible to use space-time-multiplexed illumination in a ProCam system to recover scene depth. Nonetheless, many obstacles still remain to be overcome.
Like pinhole cameras, a projector suffers from limited field-of-view, i.e., it can be difficult to produce a panoramic projection using a single projector. One possible solution is to mosaic multiple projectors, and significant advances have been made in automatic mosaicing of multiple projectors. However, these systems typically require accurate geometric and photometric calibrating between the multiple projectors and a camera.
One approach toward facilitating accurate geometric and photometric calibration of a camera and an individual projector is drawn from an article by Sen et al., entitled “Dual Photography”, published in the Proceedings ACM SIGGRRAPH, 2005, which is herein incorporated by reference in its entirety. Dual photography makes use of Helmholtz reciprocity to use images captured with real cameras to synthesize pseudo images (i.e. dual images) that simulate images “as seen” (or effectively “captured”) by projectors. That is, the pseudo image simulates a captured image as “viewed” by a projector, and thus represents what a projector-captured image would be if a projector could capture images.
Helmholtz reciprocity is based on the idea that the flow of light can be effectively reversed without altering its light transport properties. This reciprocity may be summarized by an equation describing the symmetry of the radiance transfer between incoming (ωi) and outgoing (ωo) directions as fr(ωi→ωo)=fr(ωo→ωi), where fr represents the bidirectional reflectance distribution function (BRDF) of a surface.
Thus, dual photography ideally takes advantage of this dual nature (i.e. duality relationship) of a projected image and a captured image to simulate one from the other. Dual photography (and more precisely Helmholtz reciprocity) requires the capturing of the light transport property between a camera and a projector. More specifically, dual photography requires determination of the light transport property (i.e. light transport coefficient) relating an emitted light ray to a captured light ray.
When dealing with a digital camera and a digital projector, however, dual photography requires capturing a separate light transport coefficient relating each projector pixel (i.e. every emitted light ray) to each, and every, camera pixel (i.e. every light sensor that captures part of the emitted light ray), at the resolution of both devices.
Since images projected by a digital projector and captured by a digital camera can be represented as a matrix of data, creation of a light transport matrix T relating the digital projector to the digital camera would facilitate the use of dual photography, which brings the discussion back to the subject of catadioptric optical systems.
Catadioptric optical systems are typically associated with catadioptric telescopes and catadioptric cameras, but an object of the present invention is to create a catadioptric projector.
A second object of the present invention is to provide an omni-directional projection system that uses a single projector, as opposed to those that require multiple projectors.
Another object of the present invention is to improve images created by a catadioptric projector system.